Problem: Simplify the following expression: $k = \dfrac{2x + 2}{5x + 10} - \dfrac{9x - 2}{5x + 10}$
Since the expressions have the same denominator we simply subtract the numerators: $k = \dfrac{2x + 2 - (9x - 2)}{5x + 10}$ Distribute the negative sign: $k = \dfrac{2x + 2 - 9x + 2}{5x + 10}$ Combine like terms: $k = \dfrac{-7x + 4}{5x + 10}$